In a reversible reaction, study of its mechanism says that both the forward and reverse reaction follows…

In a reversible reaction, study of its mechanism says that both the forward and reverse reaction follows first order kinetics. If the half life of forward reaction $\left(\mathrm{t}_{1 / 2}ight)_{\mathrm{f}}$ is $400 \mathrm{sec}$ and that of reverse reaction $\left(t_{1 / 2}ight)_{\mathrm{r}}$ is $250 \mathrm{sec}$. The equilibrium constant of the reaction is
  1. $1.6$
  2. $0.433$
  3. $0.625$
  4. $1.109$

Solution

$K_{f}=\frac{0.693}{400} \sec ^{-1} ; K_{r}=\frac{0.693}{250} \sec ^{-1}$
$K=\frac{k_{f}}{k_{r}}=\frac{250}{400}=0.625$

Asked in: JEE-TOPICTESTS-CHEMISTRY

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